Getting can't pickle CompiledFFI objects error upon making a deepcopy of paramiko SSH session object

I am using paramiko to make SSH connections to different VMs and somehow I have got this new requirement where I will need to make a deepcopy of the paramiko SSH session.

import copy
import paramiko
class SSH:
    def __init__(self,host, username, password, port=22):
        self.host = host
        self.username = username
        self.password = password
        self.port = port
        self.ssh = None

    def _openSSHConnection(self):

        try:
            print('Login to the host ({}) with credentials (username={},password={},port={})'.format(self.host,
                                                                                                        self.username,
                                                                                                        self.password,
                                                                                                        self.port))
            ssh = paramiko.SSHClient()
            ssh.set_missing_host_key_policy(paramiko.AutoAddPolicy())
            ssh.connect(self.host, username=self.username, password=self.password)
            self.ssh = ssh
            if self.ssh is not None:
                print(
                    'Successfully in to the host ({}) with credentials (username={},password={},port={})'.format(
                        self.host, self.username, self.password, self.port))
            else:
                print('Failed to connect on host ({}) with credentials (username={},password={},port={})'.format(
                    self.host, self.username, self.password, self.port))
        except Exception as e:
            print(
                'Failed to connect on host ({}) with credentials (username={},password={},port={})'.format(self.host,
                                                                                                           self.username,
                                                                                                           self.password,
                                                                                                           self.port))
            print(e)

    def __enter__(self):
        if self.ssh is None:
            self._openSSHConnection()

        return self
    def close(self):
        print('Exiting the SSH session from host ({})'.format(self.host))
        if self.ssh is not None:
            self.ssh.close()
            self.ssh = None
    # 
    def __exit__(self, exc_type, exc_val, exc_tb):
        self.close()

with SSH(host='10.61.1.1',username='root',password='******') as zssh:
    print(zssh)
    copy_ssh = copy.deepcopy(zssh)
    print(copy_ssh)

The above code generates the following exception:

Traceback (most recent call last):
  File "/Users/chintanvadgama/zscaler-automation/zpytest_python3/zpytest/tests/pac_check/reproduce_paramiko.py", line 72, in <module>
    copy_ssh = copy.deepcopy(zssh)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 215, in _deepcopy_list
    append(deepcopy(a, memo))
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 180, in deepcopy
    y = _reconstruct(x, memo, *rv)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 280, in _reconstruct
    state = deepcopy(state, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 150, in deepcopy
    y = copier(x, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 240, in _deepcopy_dict
    y[deepcopy(key, memo)] = deepcopy(value, memo)
  File "/usr/local/Cellar/python/3.7.6_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/copy.py", line 169, in deepcopy
    rv = reductor(4)
TypeError: can't pickle CompiledFFI objects

Environment Information:

Python 3.8.2
paramiko==2.7.1
cryptography==2.9
pycrypto==2.6.1
PyNaCl==1.3.0

Also tried the same script on another environment, it still throws a similar exception

python 3.6.8
cryptography==2.8
paramiko==2.6.0
PyNaCl==1.3.0

The report provides a standalone reproduction using paramiko.SSHClient and copy.deepcopy; start by running it against the listed Python and Paramiko environments and inspecting the object state that leads to the CompiledFFI error. Establish whether deep-copying an active SSH session is supported, then define and test the expected behavior or document the limitation.